not sure if you can add a timer element to it, but I used to play a game to identify the prefectures and I'd try to see how far under a minute I could get
I have some other thoughts for ways to expand the games, like you can add a LOT more cities (but the map would have to have more definition), and then the quiz could provide some details of the city when you click on it.. you can also quiz on the prefectural seat of each prefecture (or highlight a prefecture and then ask the user to type in the name). Other increasingly difficult quizzes could be for mountains or bodies of water or rivers, famous temples or locations, or even "listen to a snippet of this area's dialect, and then identify where it's from"